Related papers: Effective alpha theory certification using interva…
This paper considers the question of the rate of convergence to ${\alpha}$- stable laws, using arguments based on the Zolotarev distance to prove bounds. We provide a rate of convergence to ${\alpha}$-stable random variable where 1 <…
The PC algorithm infers causal relations using conditional independence tests that require a pre-specified Type I $\alpha$ level. PC is however unsupervised, so we cannot tune $\alpha$ using traditional cross-validation. We therefore…
We present a new rational approximation algorithm based on the empirical interpolation method for interpolating a family of parametrized functions to rational polynomials with invariant poles, leading to efficient numerical algorithms for…
Gappa uses interval arithmetic to certify bounds on mathematical expressions that involve rounded as well as exact operators. Gappa generates a theorem with its proof for each bound treated. The proof can be checked with a higher order…
The goal of this paper is twofold. First, we present a unified way of formulating numerical integration problems from both approximation theory and discrepancy theory. Second, we show how techniques, developed in approximation theory, work…
Quadratic form reduction and lattice reduction are fundamental tools in computational number theory and in computer science, especially in cryptography. The celebrated Lenstra-Lenstra-Lov\'asz reduction algorithm (so-called LLL) has been…
The aim of this work is to certify lower bounds for real-valued multivariate functions, defined by semialgebraic or transcendental expressions. The certificate must be, eventually, formally provable in a proof system such as Coq. The…
Data following an interval structure are increasingly prevalent in many scientific applications. In medicine, clinical events are often monitored between two clinical visits, making the exact time of the event unknown and generating…
With distributed computing and mobile applications, synchronizing diverging replicas of data structures is a more and more common problem. We use algebraic methods to reason about filesystem operations, and introduce a simplified definition…
In this article we present very intuitive, easy to follow, yet mathematically rigorous, approach to the so called data fitting process. Rather than minimizing the distance between measured and simulated data points, we prefer to find such…
A recently developed variational resummation technique incorporating renormalization group properties has been shown to solve the scale dependence problem that plagues the evaluation of thermodynamical quantities, e.g., within the framework…
Assumption-based argumentation (ABA) is a central structured argumentation formalism. As shown recently, answer set programming (ASP) enables efficiently solving NP-hard reasoning tasks of ABA in practice, in particular in the commonly…
For typical first-order logical theories, satisfying assignments have a straightforward finite representation that can directly serve as a certificate that a given assignment satisfies the given formula. For non-linear real arithmetic…
Debiased machine learning is a meta algorithm based on bias correction and sample splitting to calculate confidence intervals for functionals, i.e. scalar summaries, of machine learning algorithms. For example, an analyst may desire the…
A large class of problems in sciences and engineering can be formulated as the general problem of constructing random intervals with pre-specified coverage probabilities for the mean. Wee propose a general approach for statistical inference…
We propose a method to improve the efficiency and accuracy of amortized Bayesian inference by leveraging universal symmetries in the joint probabilistic model of parameters and data. In a nutshell, we invert Bayes' theorem and estimate the…
Alphabetic optimality criteria, such as the $D$, $A$, and $I$ criteria, require specifying a model to select optimal designs. They are not model free and the optimal designs selected by them are not robust to model uncertainty. Recently,…
This study is motivated by the recent development in the fractional calculus and its applications. During last few years, several different techniques are proposed to localize the nonlocal fractional diffusion operator. They are based on…
We consider stochastic optimization problems which use observed data to estimate essential characteristics of the random quantities involved. Sample average approximation (SAA) or empirical (plug-in) estimation are very popular ways to use…
We introduce Symbolic Alternating Finite Automata (s-AFA) as an expressive, succinct, and decidable model for describing sets of finite sequences over arbitrary alphabets. Boolean operations over s-AFAs have linear complexity, which is in…